Following [1]}, we convert this into an unconstrained optimization problem by applying the bottleneck on the Q-function representation and directly selecting the Lagrange multiplier \(\alpha \) , resulting in the full VIB objective:
\(\mathcal {L} & = & \mathcal {L}_\text{RL}-\alpha D_{KL}{\phi (z_t | s_t)}{p(z)} - \alpha D_{KL}{\phi (z_g | g)}{p(z)}\) 
